Answer:
y' = (x² + 4)eˣ
Step-by-step explanation:
Power rule: y' = f'(x)g(x) + f(x)g'(x)
[tex]\frac{d}{dx} [e^x]=e^x[/tex]
Step 1: Write equation
y = (x² - 2x + 6)eˣ
Step 2: Differentiate
- Power rule: y' = eˣ(2x - 2) + eˣ(x² - 2x + 6)
- Factor out eˣ: y' = eˣ[2x - 2 + x² - 2x + 6]
- Combine like terms: y' = eˣ(x² + 4)
- Rewrite: y' = (x² + 4)eˣ
